Some applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913493905571840 |
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| author | Leite, Edir Junior Ferreira Quoirin, Humberto Ramos Silva, Kaye |
| author_facet | Leite, Edir Junior Ferreira Quoirin, Humberto Ramos Silva, Kaye |
| contents | Given a real Banach space $X$, we show that the Nehari manifold method can be applied to functionals which are $C^1$ in $X \setminus \{0\}$. In particular we deal with functionals that can be unbounded near $0$, and prove the existence of a ground state and infinitely many critical points for such functionals. These results are then applied to three classes of problems: the {\it prescribed energy problem} for a family of functionals depending on a parameter, problems involving the {\it affine} $p$-Laplacian operator, and degenerate Kirchhoff type problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$ Leite, Edir Junior Ferreira Quoirin, Humberto Ramos Silva, Kaye Analysis of PDEs Given a real Banach space $X$, we show that the Nehari manifold method can be applied to functionals which are $C^1$ in $X \setminus \{0\}$. In particular we deal with functionals that can be unbounded near $0$, and prove the existence of a ground state and infinitely many critical points for such functionals. These results are then applied to three classes of problems: the {\it prescribed energy problem} for a family of functionals depending on a parameter, problems involving the {\it affine} $p$-Laplacian operator, and degenerate Kirchhoff type problems. |
| title | Some applications of the Nehari manifold method to functionals in $C^1(X \setminus \{0\})$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.05138 |